UW AMATH 481 (Autumn 2016)

Course website.

Course Blog

This is a weblog for the course. Announcements, notes, sample code, and homework assignments will be posted here.

Due dates:


A survey of numerical methods for the solution of problems arising in the physical sciences, with an emphasis on methods for the solution of differential equations. Topics will include: the Fourier transform, finite differences, finite elements, spectral methods, integral equation methods, and fast solution techniques.


This course requires familiarity with programming, differential equations, and linear algebra. The appropriate background at UW is: AMATH 301; either AMATH 351 or MATH 307; either AMATH 352 or MATH 308.


Instructor: Travis Askham

  • Lectures: MWF 9:30-10:20am, Denny Hall 259.
  • Office Hours: MW 10:30-11:30am, Lewis Hall 129.

Teaching Assistant: Trevor Caldwell

  • Office Hours: T 4-5pm, Lewis Hall 128.



There is no required textbook for the course. For reference, we will use the notes by Nathan Kutz provided below. I will post some additional resources in the future for those interested in further reading.

Course notes

Some good Wikipedia pages

Books (links are to Amazon but these can often be found at a university library).

Course Outline

NOTE: this outline is temporary and subject to change.

This is a 5 unit course and will contain a challenging workload. We will cover most of the material of Nathan Kutz’s notes plus some supplementary material on integral equations and approximation theory. An approximate course schedule is below and includes the dates of quizzes and the midterm. The chapters of the notes cover:

  • Chapter 1 - Initial and boundary value problems of differential equations
  • Chapter 2 - Finite difference methods
  • Chapter 3 - Time and space stepping schemes: method of lines
  • Chapter 4 - Spectral methods
  • Chapter 5 - Finite element methods


Date Day Description
9/28 W Course intro
9/30 F Section 1.1 of the notes
10/3 M (Quiz) Section 1.2 of the notes
10/5 W Section 1.3 of the notes
10/7 F Section 1.4 of the notes
10/10 M Section 1.5 of the notes
10/12 W Extra time for Chapter 1
10/14 F Extra time for Chapter 1
10/17 M (Quiz) Section 2.1 of the notes
10/19 W Section 2.2 of the notes
10/21 F Section 2.3 of the notes
10/24 M Section 2.4 of the notes - Prof. Nathan Kutz
10/26 W Section 2.5 of the notes - Video
10/28 F Section 2.6 of the notes - Prof. Nathan Kutz
10/31 M (Quiz) Extra time for Chapter 2
11/2 W Extra time for Chapter 2
11/4 F Section 3.1 of the notes
11/7 M Section 3.2 of the notes
11/9 W Midterm exam
11/11 F Veterans day. No lecture
11/14 M Section 3.3 of the notes
11/16 W Section 3.4 of the notes
11/18 F Section 3.5 of the notes
11/21 M (Quiz) Finite Element Methods (Chapter 5 and project)
11/23 W Finite Element Methods (Chapter 5 and project)
11/25 F Happy Thanksgiving! No lecture
11/28 M Chapter 4 and Chebfun
11/30 W Chapter 4 and Chebfun
12/2 F Chapter 4 and Chebfun
12/5 M (Quiz) Chapter 4 and Chebfun
12/7 W Chapter 4 and Chebfun
12/9 F Chapter 4 and Chebfun


There will be brief quizzes every other Monday at the end of lecture. These will generally cover material from the previous 3 lectures.

The lowest quiz score will be dropped. If you have a documented reason for missing a quiz (e.g. doctor’s note), up to 3 scores may be dropped. If you anticipate missing more than 3 quizzes with good reason (e.g. if you are a student-athlete with competitions on Mondays), then we will work out an alternative plan.


There will be homework assignments (roughly 6 for the quarter). Typically, the homework assignments will have reading, writing, and coding components. Collaboration is allowed and encouraged on homework assignments but you must turn in your own write-up and code.

I encourage the use of the LaTeX typesetting system for the written portion of the homework. Once learned, LaTeX allows you to efficiently typeset equations and create professional looking documents. See the important links section for some resources on this.

The homework submission process is TBD. Late homework will not be accepted.

Midterm Exam

There will be a midterm exam on Wednesday November 9th during lecture which will cover the material up to and including November 2nd. You must take the midterm on this date. Exceptions will only be granted in extreme circumstances.


The coursework related to finite element methods will take the form of a guided project. In a sense, the project is a more free-form homework assignment with one caveat: collaboration is not allowed.

The project submission process is TBD. Late project submissions will not be accepted.


The final course grade will be a combination of the scores received for quizzes, homework, the midterm exam, and the project. The components are weighted by:

  • HW: 40%
  • Quizzes: 20%
  • Midterm: 20%
  • Project: 20%

Grades will be adjusted on a per-assignment basis with the goal that an A corresponds with mastery of the material and a B corresponds with proficiency in the material. This process will only increase raw grades.

The lowest quiz score will be dropped.


We are happy to help. Due to time constraints, we suggest the following methods for obtaining help, with email, in general, as a last resort:

  • Discussion board. The discussion board is ideal for questions that you think other students may have. This includes questions about course policy (e.g. grading, exams), questions about possible typos in assignments, and questions about course material.
  • Office hours. The instructor and TA office hours are ideal for questions about course material which require more individual attention.
  • Email. Sending the instructor an email is best-suited for emergencies and personal issues (and is quite welcome in these cases). For the sake of efficiency, I will generally not answer content-related email questions. The TA’s email policy is TBD.

Academic Integrity

I take academic integrity very seriously. Students are expected to abide by the student code of conduct. Any student found engaging in academic misconduct (see 478-120-024) will receive a score of zero for the assignment in question. In particular, cheating on the midterm exam or final project may result in a failing grade for the course.


Links to various resources will be collected here.

UW details

MatLab access

You have a few options for MatLab access.

  • MatLab student copy. A student copy of MatLab can be purchased at a significant discount.
  • MatLab from UW. A temporary MatLab license from UW (cheaper, expires June 2017).
  • Remote access. MatLab can be accessed remotely through the mechanical engineering department’s remote desktop servers.
  • UW ICL. The instructional computing labs at UW have MatLab installed.
  • Octave. An open source version of MatLab. A fair option but you’re on your own for debugging. In my experience, the performance of Octave is generally slower than MatLab’s but usable.

LaTeX typesetting

For typesetting equations, I strongly recommend LaTeX.

  • Online LaTeX editor
  • Obtaining LaTeX I’ve used MikTeX on Windows and TeX Live for Linux and found both to be useful. On older versions of Windows, the standard PDF viewer doesn’t automatically refresh when you compile the LaTeX. If you’re dealing with this on Windows, I recommend Sumatra PDF.
  • LyX LyX might be a good option for people who run Windows or anyone who wants more of a WYSIWYG-like experience. Another reason to consider this option is that you don’t have to install LaTeX separately.


A few of these lists were compiled by others. Thank you:

  • Niall Mangan
  • Mark Kot


Email: [my last name] [at] uw [dot] edu